Later, [1]} implemented the conditional GAN, turning GAN to be supervised learning algorithm, where both the discriminator and the generator take an extra auxiliary label so that GAN generates images conditional on the given label according to updated objective function Eq. REF .
\(\min _{G}\max _{D}\mathbb {E}_{x\sim p_{\text{data}}(x)}[\log {D(x|c)}] + \mathbb {E}_{z\sim p_{\text{z}}(z)}[ \log {(1-D(G(z|c)))}],\) 
